Notes

Following the development of the molecular model for gases in the late 1800s (see page 1019), early mathematical derivations of continuum fluid behavior from underlying molecular dynamics were already complete by the 1920s. More streamlined approaches with the same basic assumptions continued to be developed over the next several decades. In the late 1950s Berni Alder and Thomas Wainwright began to do computer simulations of idealized molecular dynamics of 2D hard spheres—mainly to investigate transitions between solids, liquids and gases. In 1967 they observed so-called long-time tails not expected from existing calculations, and although it was realized that these were a consequence of fluid-like behavior not readily accounted for in purely microscopic approximations, it did not seem plausible that large-scale fluid phenomena could be investigated with molecular dynamics. The idea of setting up models with discrete approximations to the velocities of molecules appears to have arisen first in the work of James Broadwell in 1964 on the dynamics of rarefied gases. In the 1960s there was also interest in so-called lattice gases in which—by analogy with spin systems like the Ising model—discrete particles were placed in all possible configurations on a lattice subject to certain local constraints, and average equilibrium properties were computed. By the early 1970s more dynamic models were sometimes being considered, and for example Yves Pomeau and collaborators constructed idealized models of gases in which both positions and velocities of molecules were discrete. As it happens, in 1973, as one of my earliest computer programs, I created a simulation of essentially the same kind of system (see page 17). But it turned out that this particular kind of system, set up as it was on a square grid, was almost uniquely unable to generate the kind of randomness that we have seen so often in this book, and that is needed to obtain standard large-scale fluid behavior. And as a result, essentially no further development on discrete models of fluids was then done until after my work on cellular automata in the early 1980s. I had always viewed turbulent fluids as an important potential application for cellular automata. And in 1984, as part of work I was doing on massively parallel computing, I resolved to develop a practical approach to fluid mechanics based on cellular automata. I initiated discussions with various members of the fluid dynamics community, who strongly discouraged me from pursuing my ideas. But I persisted, and by the summer of 1985 I had managed to produce pictures like those on page 378. Meanwhile, however, some of the very same individuals who had discouraged me had in fact themselves pursued exactly the line of research I had discussed. And by late 1985, cellular automaton fluids were generating considerable interest throughout the fluid mechanics community. Many claims were made that existing computational methods were necessarily far superior. But in practice over the years since 1985, cellular automaton methods have grown steadily in popularity, and are now widely used in physics and engineering. Yet despite all the work that has been done, the fundamental issues about the origins of turbulence that I had originally planned to investigate in cellular automaton fluids have remained largely untouched.